(On the other hand, in Euros, elegance means that the game is complex but all the moving parts all fit together like clockwork. Which could mean the same thing, since you usually don't have extra gears in your pocket watch. But it doesn't feel simple so I'm calling it a different flavor of elegant.)
This is one case where the philosophy of German Family Games and Abstract Games overlaps. That simplicity is a key element to so many abstracts. Go is one of the complex games I have ever played, perhaps the most complex. But the ruleset is very minimal. Other genuine classics, like Checkers or Mancala or Hex are even more minimal. Seriously, Hex is so minimal but it is still a challenging and interesting game. But it is clearly not a German Family Game.
Part of my old definition of an abstract used to include no random elements and no hidden information. However, as I've heard many games I love Qwirkle or Ingenious described as abstracts, I've come to accept that that's too rigid a definition. However, I feel that games like Ingenious, originally introduced to me as a German Family Game, show how blurry the line between the schools can be.
One designer who I feel embraced that blurry line, probably helped create that blurry line, is Alexander Randolph. He and Sid Sackson helped guide the 3M game line back in the 1960s and 1970s, which helped develop the modern designer game. The 3M line definitely pushed the idea of games that weren't for children or for gambling but for intellectual stimulation. Oh lord, that sounded so snobby and elitist.
Many of his designs like Ghosts or Ricochet Robots or Bison or Twixt are fundamentally abstracts. Man, there is no other way to describe Twixt but as an abstract. But they were aimed at the audience that would define German Family Games. I wonder what he would make after he saw what has been designed today. (Of course, I wonder even more what Sid Sackson would design)
I do believe that these two schools of philosophy use simplicity for different reasons. The Abstract school, not always intentionally, uses minimalism to refine the game. The German Family Game school uses simplicity to make games accessible.
Abstract Games as philosophy is probably one of the most nebulous ones. After all, it includes centuries upon centuries of games that were independently developed all over the globe. So much of it comes from the natural organic development that took place over time. Minimalism necessity for games to be passed down by word-of-mouth over generations. German Family Games, on the other hand, are intentionally designed for a targeted audience.
So, when I just use the word elegant to describe a German Family Game, I guess I mean easy to teach and fun to play.